Question

A normal population has mean *μ* = 9 and standard
deviation *σ* = 6.

a. |
What proportion of the population is less than 20? |

b. |
What is the probability that a randomly chosen value will be greater than 5? |

Answer #1

Solution :

Given that ,

mean = = 9

standard deviation = = 6

a.

P(x < 20) = P[(x - ) / < (20 - 9) / 6]

= P(z < 1.83)

= 0.9664

proportion = **0.9664**

b.

P(x > 5) = 1 - P(x < 5)

= 1 - P[(x - ) / < (5 - 9) / 6)

= 1 - P(z < -0.67)

= 1 - 0.2514

= 0.7486

Probability = **0.7486**

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(b) What is the probability that a randomly chosen value will be
between 35 and 45?
Round the answers to at least four decimal places.

A normal population has mean μ=40 and standard deviation σ
=9.
(a) What proportion of the population is between 20 and 30 ?
(b) What is the probability that a randomly chosen value will be
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Round the answers to at least four decimal places

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Round the answers to at least four decimal places.

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Round the answers to four decimal places.

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A normal population has mean
μ
=
52
and standard deviation
σ
=
7
. What is the
82
nd percentile of the population?

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